11 questions. Tap an option to check it instantly, then read the solution.
Practice SSC JE and other civil engineering exam questions on moments: moment of a force, moment at a hinge, first and second moment of area, centroids of composite sections, moment of inertia of rectangles, triangles, circles and semicircles, the parallel and perpendicular axis theorems, polar moment of inertia and mass moment of inertia. Tap an option to check it, then open the full explanation for each question.
Question 1Medium
For a semicircular plate of diameter D and radius R, with y as the vertical axis and x as the horizontal axis passing through the diameter, the moment of inertia about the y-axis will be:
About its diameter or its axis of symmetry, a semicircle has half the moment of inertia of the full circle: ½ × πD⁴/64 = πD⁴/128.
Question 2Medium
Locate the centroid, measured from the base AB, of a rectangular section 200 mm wide and 300 mm high from which a circle of diameter 150 mm, centred 100 mm below the top edge, has been removed.
Answer: C. The first moment of area may be either negative or positive depending on the chosen reference axes, but the second moment of area is always positive.
First moment ∫y dA can be +, − or 0 depending on the axis; second moment ∫y² dA uses squared distances, so it is always positive.
Question 4Medium
The polar moment of inertia of a semicircular lamina of radius R about its central axis (through the centre of the diameter, perpendicular to the plane) is:
ω = dθ/dt; angle is dimensionless, so ω has dimension T⁻¹.
Question 9Easy
The moment of inertia of a circular area about its diameter is Ixx. The moment of inertia of the same area about an axis perpendicular to its plane (through the centre) is Izz. Which statement is correct?